Working with Single-Angle Members: The inherent eccentricities of this popular shape require the engineer’s attention and understanding

ANGLES HAVE BEEN USED in construction almost as long as structural steel has been around, and were commonly used as components of built-up shapes. For example,

Bethlehem Steel made I-shaped members and channels using angles attached to plates. Other producers used them to build similar cross sections and other more exotic shapes.

More recently, angles have been used as braces, tension members, struts and lintels. Angles also have been used in double-angle and single-angle connections.

In spite of their long history of usage, the design of members composed of angles-and single angles in particular-has not become as familiar to the engineering profession as the design of other, more common shapes. This article highlights the information available today to help in this regard.

The AISC Specification

AISC first published a single-angle specification in the

1980s. Since then more research and testing has helped to develop the knowledge base upon which single-angle design is covered in the 2005 AISC Specification (and the soon-to-be-released 2010 AISC Specification).

The current approach to single-angle design offers two alternatives:

1. A comprehensive design approach that can be used to design any single angle for axial and/or flexural loads.

This approach is more general and involves more effort in calculations that typically are based upon the principal axes.

2. A simplified design approach that can be used with greater expediency for specific common cases. Although limited in scope, it allows an easier design process.

Principal Axes

The principal axes of any shape define two orthogonal axes that correspond to the maximum and minimum moments of inertia for that section. The axis around which one finds the minimum moment of inertia is called the minor principal axis while the axis about which one finds the maximum moment of inertia is called the major principal axis. From a structural analysis point of view, bending the section about the minor principal axis corresponds with the minimum internal energy of the member. This means the structure is completely stable when bent about this axis and cannot experience lateral-torsional buckling.

Unlike singly and doubly symmetric wide-flanges and channels, single angles have principal axes that do not coincide with their geometric axes (see Figure 1). Therefore, the design of single angles requires some consideration of both of these sets of axes. While loading typically occurs about the geometric axes, the strength usually is controlled by response that is influenced by properties that relate to the principal axes.

Part 1 of the AISC Manual contains properties of single angles about both geometric axes (X and Y) and the minor principal axis (Z). Part 17 of the AISC Manual contains equations that allow for the calculation of section properties about one axis when the properties are known about the other.

 

The importance of evaluating section properties about the principal axes for single angles is illustrated in Figure 2.

Consider a single angle that is bent about the geometric axis and not braced against lateral deformation other than at the ends.

As the beam is loaded, it tends to naturally deflect in the direction of the load. However it also tends to deflect in the direction of least resistance, which corresponds with the minor principal axis.

This results in a total deflection that occurs in the direction of both geometric axes. For such cases it is difficult to evaluate first yield or the propensity of the member to laterally buckle without resolving the load and response into components that are parallel to the principal axes. Something similar can be said of an axially loaded single angle. Its tendency to fail in Euler flexural buckling will be about the axis of least resistance which corresponds with the minor principal axis.

 

Other Important Section Properties

If the evaluation of the moment of inertia of single angles about the principal axes is important, the evaluation of the section moduli about the same axes is even more useful. Additionally, it is important to recognize that the single angle can have as many as three section moduli about one axis. For unequal-leg angles two correspond to the toes of the legs while one relates to the heel.

When evaluating unequal-leg single angles for combined axial and flexural loading, this can make the calculation quite lengthy.

Several articles published in AISC’s Engineering Journal provide further insight into working with single-angle members: “Evaluating Single-Angle Compression Struts Using an Effective Slenderness Approach,” by Leroy A. Lutz (4th Quarter 2006), “Towards the Simplified Design of Single-Angle Beam Columns,” by Christopher J. Earls and D. Christian Keelor (1st Quarter 2007), and “Design of Single Angles Bent About the Major Principal Axis,” by Christopher J. Earls. All are available at www.aisc.org/epubs as free downloads to AISC members and may be purchased by others.

Another Reference

In addition to the information available in the AISC Specification and Manual, Whitney

McNulty, P.E., recently self-published a guide to single-angle design called the Single-Angle Design Manual. It is devoted to the specifics of the design of angles and has chapters that get into the details of equal-leg and unequalleg single angles in tension, shear, compression, and flexure (including interaction). The interested reader can find this reference at www.lulu.com/singleangle.

Conclusion

The design of single angles is more complicated than that of other more common shapes. Nonetheless, the versatility of single angles in construction has made them popular.

Provisions and recommendations exist in the AISC Specification, AISC Manual, and other references to assist the engineer who wants to design single angles.

Three things you should get straight about curved steel

THE USE OF CURVED STEEL as an integral part of structural systems has continued to grow in recent years.

Analysis tools have become more sophisticated and Measier to use, as well as more affordable and accessible, making it easier for engineers to incorporate curved steel into their structural designs. And the same time, owners and other stakeholders, such as tenants and community residents, have become more aware of the possibilities curved steel offers. The desire for its aesthetic contributions also has increased.

Projects that take advantage of curved steel elements can include anywhere from a few pieces used in strategic locations to a large percentage of the project’s framing.

One example of the large-scale use of curved steel is the recently topped out Kauffman Center in Kansas City, Mo., where more than 20% of the structural steel is curved. (See the project article on page 24 of this issue.)

The reasons for incorporating curved steel include appearance, convenience and simply the designer’s preference. For example, the trend in stadium design toward cantilevered and long-span construction to provide column-free, unobstructed views has proved to be a good application for curved steel. It also has led to requests to bend larger, more massive members to achieve these open spaces.

As more people on the design side become involved in designing with and specifying curved steel, the need for practical information also has become more widespread.

AISC and others offer a good amount of reference material on the subject of curving steel (see sidebar), but with new engineers joining the market for curved steel, there always are people on the steep part of the learning curve.

We recently asked three long-time professionals from the

Milwaukee-based bender-roller Max Weiss Co. LLC to help clear up some common misconceptions associated with this process. Here is a summary of the information provided by president Daniel Weiss, operations manager

Al Sanders, and senior estimator Dave Nader.

Common Misconception #1: It’s easier to bend steel members the easy way as opposed to the hard way.

The terminology referring to bending the “easy way” and the “hard way” simply refers to the relative amount of force required to bend a member about its weak axis versus its strong axis. However, controlling the corollary effects is often what increases the difficulty of bending a given member.

For example, depending on how tight the radius is, bending a wide-flange member the hard way may result in less need to control flange distortion than would be required if it were being bent the easy way.

Although bender-rollers have developed general tables on the curvature limits for various standard sizes and shapes, the bending itself still requires a significant amount of human oversight and judgment. The operator’s skill is what makes the difference between a successfully curved member and having to try again.

Common Misconception #2: Heavier material is harder to curve than lighter material.

Although it may take less force to bend a lightweight member than one that is heavier, it also requires more control and the operator’s increased attention. Distortion is more difficult to control in thinner-walled material than when the material is thicker. One good example is HSS, where it also is almost always easier to keep the sides from rippling or becoming otherwise distorted when bending the hard way.

One of the reasons this is a concern is that lighter shapes often are being used for architectural effect. Where the steel will be exposed to view and appearance is important, minimizing distortion is also important. Experienced bender-rollers know how to prepare the steel and work with it to achieve the desired curvature without the undesirable side effects.

Common Misconception #3: All the bender-roller needs to know from the architect or engineer are the dimensions and orientation for each piece—a radius and a length, and whether to bend the hard way or the easy way.

On the contrary, providing the bender-roller with as much information as possible up front decreases the number of requests for information and increases the probability of problem-free projects. Often the bender-roller’s experienced staff can suggest small changes in material sizing or selection that can improve the economics and the end result of bending.

Trust the bender-roller to help you plan for successful results.

Finally, as in all such cooperative ventures, involve the bender-roller as early in the process as possible. Again, their experience can help you navigate the predictable twists and turns in the process of working with curved steel.

Saving time in Tall Wall Contruction

AS HEAD DESIGN engineer for TF System, Inc., Jerry Spude both designs insulated concrete forms (ICFs) and oversees their construction on large projects. For the past 15 years, the Green Bay, Wis.-based company has produced ICFs and sold them through its network of distributors. The stay- in-place forms have been used for a wide range of commercial, residential, and institutional buildings.

Unlike most ICF systems, the TF form segments are oriented vertically, which makes them especially well suited for tall walls. The system consists of four main components:
• Panels made of 2½ -in.-thick, highdensity, rigid polystyrene.
• Corner sets made of rigid, recycled
PVC.
• Stud rails available in either rigid, recycled PVC (standard) or 26-gauge galvanized steel.
• C-channels made of 27-gauge galvanized and painted steel.

The vertical orientation is designed to prevent the wall forms from floating and settling, and to provide a dimensionally accurate wall. With no need to glue, tape, or tie components together, assembly is simple and efficient. The basic components form the walls, provide insulation, create a vapor barrier, and serve as convenient and predictable attachment points.
The TF System requires no special concrete mix design beyond a recommendation to use a 4- to 6-in, slump and aggregates of 3/4 in. or smaller, to make sure concrete flows freely around the stud rails. The concrete should he placed in approximately 4 foot lifts.
Contractors typically consolidate concrete in the system using the same techniques as with any other form, though Spude says that TF’s foam panels are sturdier and less prone to blowouts than some lighter-duty residential ICFs.
The company is currently managing Construction of 120, 000-sq. -ft. residence in Highlandville, Mo., that Spude describes as a “modern-day castle” with some walls that are 16 ft tall. To facilitate the consolidation of the lower 8 ft of wall (the first two lifts), the contractor is using a Rehar Shaker, manufactured by Oztec Industries, Port Washington, N.Y. These tall walls contain No. 5 vertical reinforcing bars, 16 in. on center.
To operate, one person attaches the shaker to the top of the bar, centers the bar in the wall cavity, and turns on the shaker while the concrete is placed. The vibration of the rebar serves to eliminate voids and consolidate the concrete, much as the steel or rubber head does when using a conventional pencil vibrator.
“This is our first job using the rebar shaker,” Spude says, “and it’s saving a lot of man-hours and shoulder strain. The crews don’t have to move the vibrator up and down during the pour, so it’s quite a bit easier for them. After the first two lifts, we’re using standard insertion-head vibrators to consolidate the tops of the walls. This method seems well suited for tall concrete wall construction, whether it’s with ICFs or other types of forms.”

With forms braced, crews direct pumped concrete betweem foam panels.

To operate the rebar shaker, one person attaches it on top of the bar, centers the bar in the wall cavity. And turns on the shaker while the concrete is placed.

The TF System Inc.’s vertical ICF design consists of polystyrene foam panels, steel or recycled PVC stud rails, corner sets, and C-channels.

Vibration techniques

Vibrators are easy to operate, although getting good consolidation requires a knowledgeable craftsman. Some European countries actually require vibrator operators to he licensed. Here are few tips to improve consolidation:

• Do not use vibrators to move Concrete horizontally—this can result in separation of the aggregate from the paste (segregation). Vibrators can, however, he used to “melt” a pile of concrete that was placed by bucket or buggy.
• Keep lifts in walls and columns less than 20 inches thick or about the same as the length of the vibrator head.
• The critical questions for the vibrator operator are how far apart to insert the vibrator and how deep to penetrate into the preceding lift.

• Vibrators should he sized and positioned to ensure that all concrete within the forms falls within the radius of influence (see Fig. 1). Use the largest vibrator that will fit between the reinforcement. The center-to- center distance between vibrator insertions should be 1 ½ times the radius of influence of the vibrator.
• Lifts should he placed while the preceding lift is still soft enough to penetrated by the vibrator. If that’s impossible, vibrate near the cold joint hut realize that a lift line will be visible.
• A graphical technique can help to determine how deep to penetrate into the preceding lift. Knowing that the vibration waves slope up at about a 30 degree angle from the tip, place a 30-60-90 triangle at the midpoint between  the insertion points and measure the depth of revibration into the preceding lift and then the total insertion depth (see Fig. 2). Making sure that the boundary between lifts is vibrated will knit together the lifts and eliminate lift lines in the concrete.
• Insert the vibrator as quickly as possible to the proper depth into the previous lift. Typically it will sink under its own weight.
• Hold the vibrator at its maximum depth for S to 1S seconds. Withdraw it at 3 in./second for structural concrete or 2 in./second for architectural concrete (these are the withdrawal rates recommended by AC! 309). Slow withdrawal allows the vibrator to stay below the escaping air forcing it up and out of the concrete.
• Moving the vibrator up and down slightly closes the hole behind the vibrator.
• Make sure the vibrator head remains vertical—don’t force it in at an angle.
• Don’t force the vibrator into congested reinforced concrete because you can end up with a vibrator that is stuck in the reinforcement.

• Proper consolidation is often a judgment call—experienced operators can tell if they are getting good consolidation by the sound of the vibrator.
• Despite all this, if you still have hug holes in the concrete surfaces (after stripping the forms), reduce the distance between insertion points by 20% to 30% below the standard 1½ times the radius of influence. If there are still some hug holes try spading near form surfaces
• Do not let the vibrator tip contact the form surfaces—this can damage the form panels. Rubber vibrator head tips can help reduce this potential damage.
• After the concrete surface has
stopped bleeding, revibration can he used to remove air pockets in the top lift. Don’t revibrate deeper than about 3 feet and also not with very stiff or harsh mixes.
• For exposed architectural concrete, experiment with vibration techniques to avoid color variations on the surface. For more information, read Guide to Cast-in-Place Architectural Concrete Practice, ACI 303 R-04. 

 

FIGURE 1 Use the proper size of vibrator and keep vibrator insertions

at 1 ½ time the radius of influence

 

FIGURE 2 A graphical technique can help in determining howdeep the vibrator shoul penetrate into the preceding lift.